Solutions to Fractional <i>q</i>-Kinetic Equations Involving Quantum Extensions of Generalized Hyper Mittag-Leffler Functions

Abstract

This manuscript focuses on new generalizations of q-Mittag-Leffler functions, called generalized hyper q-Mittag-Leffler functions, and discusses their regions of convergence and various fractional q operators. Moreover, the solutions to the q-fractional kinetic equations in terms of the investigated generalized hyper q-Mittag-Leffler functions are obtained by applying the q-Sumudu integral transform. Furthermore, we present solutions obtained as numerical graphs using the MATLAB 2018 program.

Keywords

• generalized hyper <i>q</i>-Mittag-Leffler functions
• fractional <i>q</i>-kinetic equation
• <i>q</i>-Sumudu transform